Tamim Iqbal made 49 and Shakib Al Hasan was 38 not out at tea as the Tigers generally applied themselves well having been put in.
Keegan Meth claimed one for 22 from 15 tidy overs, with Shingi Masakadza taking one for 41.
Openers Tamim and Jahurul Islam put on 44 before the latter, who had made a watchful 24 in seeing off the new ball, tried to break the shackles but lifted Meth to cover where Max Waller judged the catch well.
Mohammad Ashraful made just four before miscuing a hook at Masakadza, the ball skewing off the toe end straight to Graeme Cremer in the gully.
Tamim pushed on in company with Mominul Haque, the pair adding 31 before lunch, but the opener was too desperate to reach his half-century and was run out by Masakadza after taking a tight single to mid-off.
And having taken a wicket and a run-out, Masakadza added a catch when Mominul, on 23, tried to punch Elton Chigumbura through the covers.
That made it 125 for four not long after lunch, but Shakib and captain Mushfiqur Rahim batted through the remainder of the session in an unbroken stand of 46.